Research On Logical Stochastic Resonance In The Nonlinear Systems

With the development of large scale integration (LSI), all the famous chip production companies are keeping challenge the limit of the technology of chip production. The 34nm technology has already used in the newest computer, and just a few days ago, Intel has announced that they are focus on investigating the less than 10nm technology. Continuously improvement of the chip production technology provides us faster computation and portable device. However, as the technology of chip production comes to nanometer era, the effect of noise becomes tremendous and hard to eliminate. LSI, which is consisted by transistors, faces the triangle restricted relationship of size, energy consumption and precision. How to filter noise and increase the signal-to-noise ratio is the focus point of the related researchers. But noise is not always detrimental. Sometimes noise has the beneficial effect. Stochastic resonance, wherein the interplay of nonlinear system and noise can help to enhance the responses to the feeble input signal, is the typical example of the phenomena. The concept of stochastic resonance is proposed by Benzi et al. in 1981, and it has attracted immense focus from researches ever since. Phenomenon analogues to stochastic resonance are continued to be found in kinds of systems, range from optical to neuro systems. Recently, Murali et al. introduced the concept of logical stochastic resonance (LSR), namely the phenomenon where a nonlinear system driven by weak signals representing logic inputs under optimal noise can obtain logic outputs, which is an application of SR in logic computation. LSR has pointed out the new way in the paradigm of future computation, and can help to remove the triangle restricted relationship. So it has far-reaching meaning.In this paper, we use number stimulation, circuit experiments and several other methods together to investigate the characteristic of logical stochastic resonance in bistable system. The main results are listed below:First of all, we discuss how to get adaptive LSR by modulating the parameters of nonlinear system. The effects of linear and nonlinear coefficients of a quartic-bistable system on the system's response to feeble input signals in noisy background are investigated. Genetic Algorithm is applied to search for the optimal system parameters in given noise. The success probability of obtaining desired logic output is used as the fitness function. Experimental results show that the system can achieve robust logic operation in a wide range of noise intensity by adjusting the parameters.Secondly, the concept of LSR is studied in a completely noise-free situation, with the role of the thermal noise being taken by periodic forcing, especially sinusoidal forcing. The effects of amplitude, angular frequency and original phase of the periodic forcing on two types of bistable nonlinear systems are shown. LSR phenomenon is induced by changing the amplitude at given angular frequency of the periodic forcing. Further, we prove periodic forcing is better than Gaussian noise to induce the system get robust logic operation in the strong noisy background. But the correct probability of getting desired logic operation evolves periodically as we tune the angular frequency which means typical LSR phenomenon cannot be obtained by tuning angular frequency. We doubt the correctness of [PHYSICAL REVIEW E 84,055201(R) (2011)] which claimed there exists threshold of the angular frequency between which the system can obtain clear logic operation and point out the essential errors in their derivation. The step response theorem is applied to explain the influence of the periodic forcing on the outputs of the system.Thirdly, we examine the possibility of obtaining Set-Reset latch logical operation in a symmetric bistable system subjected to OU noise. The approximate Fokker-Planck equation is obtained by decoupling approximation. And the effect of correlation time and the noise intensity on the outcome is investigated by numerical stimulation.In the presence of a-stable noise, LSR phenomenon in a class of double well nonlinear system is investigated in this paper. LSR effect is obtained under a-stable noise. We examine how the four main parameters of a-stable noise influence the responses of the system. The fractional Fokker-Planck equation is presented to show when the characteristic exponent of a-stable noise is less than 1, LSR behavior will not be obtained irrespective of the setting for other parameters.Then we examine the possibility of obtaining logic operation in a quartic-bistable system with time-delayed feedback, subjected to Gaussian noise. The effect of different type of time-delayed feedback on the effective potential well is investigated and explicit numerical stimulation is carried out to study the influence of delay time and strength of the time-delayed feedback on the responses of the system. It is proved that the high order time-delayed feedback has different influence on the system compared with the low order time-delayed feedback.A circuit which is consisted by 4 amplifiers, multipliers, delay block, and several linear resistors and capacitors is introduced to implement bistable potential system with time-delayed feedback, This circuit is simple, robust, and capable of operating in very high frequency regime.The concept of LSR is applied to realize Set-Reset latch in a synthetic gene network derived from a bacteriophage ?. Clear Set-Reset latch operation is obtained when the network is interfered by periodic forcing. At the same time, we indicate that adding moderate periodic forcing to the background Gaussian noise may increase the length of the optimal plateau of getting desired logic operation in genetic regulatory network and point out that robust Set-Reset latch operation can be obtained by using the interplay of periodic forcing and background noise when the noise strength is lower than needed.